Page ?? #?-?? ANSWERS Student Learning Goal Chart Lesson Reflections

Page ?? #?-?? ANSWERS

Student Learning Goal Chart

Lesson Reflections

Pre-Algebra Learning Goal

Student will understand rational and real numbers.

Students will understand rational and real numbers by being able to do the following:

• Learn to write rational numbers in equivalent forms (3.1)• Learn to add and subtract decimals and rational numbers

with like denominators (3.2)

Pre-Algebra

3-2 Adding and Subtracting Rational Numbers

Today’s Learning Goal Assignment

Learn to add and subtract decimals and rational numbers with like denominators.

Pre-Algebra


ADDING AND SUBTRACTING WITH LIKE DENOMINATORS

Words Numbers

To add or subtract rational numbers with the same denominator, add or subtract the numerators and keep the denominator.

= , or – –2 7

2 7

4 7+ – =

2+(–4) 7

2 7

Pre-Algebra



Words Algebra


= –+a d

a + b d

b d

Pre-Algebra


Pre-Algebra


Simplify.

1. –1.2 + 8.4

2. 2.5 + (–2.8)

7.2

–0.3

3.

4. 62.1 + x for x = –127.0

1 2

–3 4

+ 5 4

–

–64.9

Lesson Quiz: Part 1

Evaluate.

Pre-Algebra


Sarah’s best broad jump is 1.6 meters, and Jill’s best is 1.47 meters. How much farther can Sarah jump than Jill?

Lesson Quiz: Part 2

5.

0.13m

Pre-Algebra


Are you ready for the FAST Track?

If YES, prepare for Ch. 3 Section 5 YES, Ch. 3 Section FIVE!

If NO, continue with the Ch. 3 Section 2 lesson!

Pre-Algebra


Pre-Algebra HW(3-1, 3-2)

Page 119#1-21 all

Pre-Algebra

3-2 Adding and Subtracting Rational Numbers3-2 Adding and Subtracting

Rational Numbers

Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra


Warm UpDivide.

1. 2.

3. Write each decimal as a fraction in simplest form.

4. 1.15 5. –0.22

21

14

24

56

12

30

2 5

1 1 2

3 7

1 3 20

– 11 50

Pre-Algebra


Pre-Algebra


Problem of the Day

Four sprinters run a race. In how many different ways can they arrive at the finish line, assuming there are no ties?24

Pre-Algebra


Today’s Learning Goal Assignment

Learn to add and subtract decimals and rational numbers with like denominators.

Pre-Algebra


The 100-meter dash is measured in hundredths of a second, so runners must react quickly to the starter pistol.

If you subtract a runner’s reaction time from the total race time, you can find the amount of time the runner took to run the actual 100-meter distance.

Pre-Algebra


In August 2001 at the World University Games in Beijing, China, Jimyria Hicks ran the 200-meter dash in 24.08 seconds. Her best time at the U.S. Senior National Meet in June of the same year was 23.35 seconds. How much faster did she run in June?

She ran 0.73 second faster in June.

24.08–23.35

0.73Align the decimals.

Additional Example 1: Sports Application

Pre-Algebra


Tom ran the 100-meter dash in 11.5 seconds last year. This year he improved his time by 0.568 seconds. How fast did Tom run the 100-meter dash this year?

Try This: Example 1

Tom ran the 100-meter dash in 10.932 seconds this year.

Subtract 0.568 from 11.5 to determine the new time.

10.932–0.56811.5 Add 2 zeros so the

decimals align.00

Pre-Algebra


A. 0.3 + (–1.2)

Move right 0.3 units.

0.4–1.0 –0.4 0

From 0.3, move left 1.2 units.

–1.2

0.3

Use a number line to find the sum.

Additional Example 2A: Using a Number Line to Add Rational Decimals

–1.4

You finish at –0.9, so 0.3 + (–1.2) = –0.9.

Pre-Algebra


0

1 5

+ 2 5

1 5

2 5

1 5

3 5

2 5


Additional Example 2B: Using a Number Line to Add Rational Decimals

Move right units. 1 5

B.

4 5

1

You finish at , so

1 5

+ 2 5

3 5

= .

3 5

From , move right units.1 5

2 5

Pre-Algebra


A. 1.5 + (–1.8)

Move right 1.5 units.

1.6–0.4 0 0.8

From 1.5, move left 1.8 units.

–1.8

1.5


Try This: Example 2A

You finish at –0.3, so 1.5 + (–1.8) = –0.3.

0.4 1.4

Pre-Algebra


0

3 8

+1 8

3 8

1 8

1 8

3 8

1 4

1 2

5 8

B.

Try This: Example 2B


Move right units. 3 8

From , move right units.3 8

1 8

You finish at ,

which simplifies to . 1 2

4 8

Pre-Algebra



Words Numbers


= , or – –2 7

2 7

4 7

+ – =2+(–4)

72 7

Pre-Algebra



Words Algebra


= –+a d

a + b d

b d

Pre-Algebra


Additional Example 3: Adding and Subtracting Fractions with Like Denominators

Subtract numerators. Keep the denominator.

2 9

– – 5 9

2 9

– – 5 9

= –7 9

= 3 7

6 7

+ – 3 7

–2 – 5 9

=

6 + (–3) 7

=

can be written as . – 3 7

–3 7

Add or subtract.

6 7

+ –3 7

A.

B.

Pre-Algebra


= 1 9

5 9

+ – 4 9

5 + (–4) 9

=5 9

+ –4 9

Try This: Example 3

Subtract numerators. Keep the denominator.

1 5

– – 3 5

1 5

– – 3 5

= – 4 5

–1 – 3 5

=

Add or subtract.

A.

B. can be written as . – 4 9

–4 9

Pre-Algebra


A. 12.1 – x for x = –0.1

Substitute –0.1 for x.12.1 – (–0.1)

12.2 Think: 12.1 – (–0.1) = 12.1 + 0.1

Evaluate the expression for the given value of the variable.

Additional Example 4A: Evaluating Expressions with Rational Numbers

Pre-Algebra


4 5= 3

+ 7 10

31 10

Add numerators, keep the denominator.

7 + 31 10

Simplify.

+ m for m = 3 7 10

1 10

38 10

=

+ 3 7 10

1 10

Substitute 3 for m.1 10

3(10) + 1 103 = =

31 10

1

10

B.


Additional Example 4B: Evaluating Expressions with Rational Numbers

Pre-Algebra


52.3 – y for y = –7.8

Substitute –7.8 for y. 52.3 – (–7.8)

60.1 Think: 52.3 – (–7.8) = 52.3 + 7.8

Try This: Example 4A

A.


Pre-Algebra


+ 5 8

47 8

Add numerators, keep the denominator.

5 + 47 8

Simplify.

+ m for m = 5 5 8

7 8

52 8

=

+ 5 5 8

7 8

Substitute 5 for m.7 8

5(8) + 7 85 = =

31 8

7 8

B.

Try This: Example 4B


1 2= 6

Pre-Algebra


Simplify.

1. –1.2 + 8.4

2. 2.5 + (–2.8)

7.2

–0.3

3.

4. 62.1 + x for x = –127.0

1 2

–3 4

+ 5 4

–

–64.9

Lesson Quiz: Part 1

Evaluate.

Pre-Algebra


Sarah’s best broad jump is 1.6 meters, and Jill’s best is 1.47 meters. How much farther can Sarah jump than Jill?

Lesson Quiz: Part 2

5.

0.13m

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Page ?? #?-?? ANSWERS Student Learning Goal Chart Lesson Reflections